Coronal heating by the resonant absorption of Alfven waves: The effect of viscous stress tensor

Details Coronal heating by the resonant absorption of Alfven waves: The effect of viscous stress tensor Coronal heating by the resonant absorption of Alfven waves: The effect of viscous stress tensor

Jan 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994apj...421..360o&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 421, no. 1, p. 360-371

Physics

73

Magnetohydrodynamic Waves, Magnetohydrodynamics, Radiation Absorption, Solar Corona, Stress Tensors, Viscosity, Solar Magnetic Field, Solar Physics, Velocity

Scientific paper

The time-dependent linearized magnetohydrodynamics (MHD) equations for a fully compressible, low-beta, viscoresistive plasma are solved numerically using an implicit integration scheme. The full viscosity stress tensor (Braginskii 1965) is included with the five parameters etai i = 0 to 4. In agreement with previous studies, the numerical simulations demonstrate that the dissipation on inhomogeneities in the background Alfven speed occurs in a narrow resonant layer. For an active region in the solar corona the values of etai are etao = 0.65 g/cm/s, eta1 = 3.7 x 10-12 g/cm/s, eta2 = 4 eta1, eta3 = 1.4 x 10-6 g/cm/s, eta4 = 2 eta3, with n = 1010/cu cm, T = 2 x 106 K, and B = 100 G. When the Lundquist number S = 104 and R1 much greater than S (where R1 is the dimensionless shear viscous number) the width of the resistive dissipation layer dr is 0.22a (where a is the density gradient length scale) and dr approximately S-1/3. When S much greater than R1 the shear viscous dissipation layer width dr scales as R1-1/3. The shear viscous and the resistive dissipation occurs in an overlapping narrow region, and the total heating rate is independent of the value of the dissipation parameters in agreement with previous studies. Consequently, the maximum values of the perpendicular velocity and perpendicular magnetic field scale as R1-1/3. It is evident from the simulations that for solar parameters the heating due to the compressive viscosity (R0 = 560) is negligible compared to the resistive and the shear viscous (R1) dissipation and it occurs in a broad layer of order a in width. In the solar corona with S approximately equals 104 and R1 approximately equals 1014 (as calculated from the Braginskii expressions), the shear viscous resonant heating is of comparable magnitude to the resistive resonant heating.

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